You'll only need to use the vector EPS if a printer requests an EPS file, or if you want to make further alterations to your logo. The vector EPS can be opened in tools like Sketch and Illustrator, which your printer should already have to access your file.
The SVG files can be used in both Sketch and Illustrator as well as GIMP. They are easily editable as they are a layered file, so if you have the design tools you can rearrange them.
SVGs can also be used on CSS enabled websites, though they have to be directly applied into the code, and cannot be added as easily as PNG files.
If you'd like to learn more about the file types and how to open them, click here.